In 1831, Michael Faraday wrapped two wires around opposite sides of an iron doughnut and found that if he passed a current through one, it immediately induced a current in the other. Faraday’s law of induction has since became a fundamental principle of electromagnetism and the operating law behind electrical transformers.
That’s of more than passing interest to physicists studying the properties of space-time. It turns out that the equations of general relatively are formally analogous to Maxwell’s laws of electromagnetism (at least, when they are studied in the weak, linear limit).
So all the results from classical electrodynamics can be equally applied to general relativity. This allows astrophysicists to define electrogravitic and gravitomagnetic fields that are analogous to electric and magnetic fields. And this kind of thinking has led to a number of predictions such as the well known frame-dragging effect in which space-time is dragged by a massive spinning object.
But today, John Swain at Northeastern University in Boston points out that despite the extensive work in this area, nobody has translated the simple idea of Faraday’s electrical transformer into the gravitational domain, an oversight that he now corrects.
The analogy to a primary winding in Swain’s model is a beam of particles traveling in a circle. This generates a “magnetogravitic flux” that can be picked up by a secondary winding, essentially a giant loop antenna.
That’s an interesting idea that raises all kinds of questions about the nature of space-time. For example, an electromagnetic transformer requires a core, a doughnut of iron, thats properties are defined by its magnetic permeability. What manner of stuff might play the role of this core in a gravitational transformer and what on Earth might be gravitational permeability?
Then there’s the question of where in the universe these kinds of transformers might exist. It’s possible that the orbit of matter close to a black hole might provide the right kind of mass-energy currents.
And on Earth, it might just be possible that the Large Hadron Collider could produce mass-energy currents that are large enough to test the idea. How might the effect manifest itself?
We know that the LHC produces large amounts of electromagnetic synchrotron radiation as the paths of its charged particles are bent into a circle. Swain suggests that his idea could be tested by looking for “gravitational synchrotron radiation”. In other words, near field gravitational wave effects that could be picked up by sensitive interferometers or Weber-type resonant bars.
Swain says there’s as much reason to imagine a gravitational analogue to permeability as there is to think that permeability itself ought to exist–after all there is no way to derive the permeability of a material from first principles.
As he says himself: “Only experiment can tell!”
Ref: arxiv.org/abs/1006.5754: Gravitatomagnetic Analogs of Electric Transformers